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Last updated at Dec. 24, 2019 by Teachoo

Transcript

Example 2 If ∠ B and ∠ Q are acute angles such that sin B = sin Q, then prove that ∠ B = ∠ Q. Given: sin B = sin Q To prove: ∠ B = ∠ Q Proof: Let’s take two right angle triangles ABC & PQR Since, sin B = sin Q 𝐴𝐶/𝐴𝐵=𝑃𝑅/𝑃𝑄 𝐴𝐶/𝑃𝑅=𝐴𝐵/𝑃𝑄 Let 𝐴𝐶/𝑃𝑅=𝐴𝐵/𝑃𝑄= k So, AC = k PR & AB = k PQ Now, Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 Now, 𝐵𝐶/𝑄𝑅 = √(𝐴𝐵2 −𝐴𝐶2)/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅= √((𝑘𝑃𝑄)2−(𝑘𝑃𝑅)2)/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅= √(𝑘2 𝑃𝑄2− 𝑘2𝑃𝑅2)/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅= (𝑘√(𝑃𝑄2−𝑃𝑅2))/√(𝑃𝑄2 −𝑃𝑅2) 𝐵𝐶/𝑄𝑅 = k From (1) and (2) 𝐴𝐶/𝑃𝑅 = 𝐴𝐵/𝑃𝑄 = 𝐵𝐶/𝑄𝑅 = k 𝐴𝐶/𝑃𝑅 = 𝐴𝐵/𝑃𝑄 = 𝐵𝐶/𝑄𝑅 Hence, corresponding sides of Δ ABC & Δ PQR are in the same ratio Thus, ∆ ABC ~ ∆ PQR So, ∠ B = ∠ Q Hence proved

Examples

Example 1

Example 2 Important You are here

Example 3

Example 4

Example 5 Important

Example 6

Example 7 Important

Example 8 Important

Example 9 Deleted for CBSE Board 2022 Exams

Example 10 Important Deleted for CBSE Board 2022 Exams

Example 11 Important Deleted for CBSE Board 2022 Exams

Example 12

Example 13 Important

Example 14 Important

Example 15 Important

Chapter 8 Class 10 Introduction to Trignometry (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.